Higgs $\to \mu \tau$ in Abelian and Non-Abelian Flavor Symmetry Models

We study lepton flavor violating Higgs decays in two models, with the recently found hint for Higgs $\to \mu \tau$ at CMS as a benchmark value for the branching ratio. The first model uses the discrete flavor symmetry group $A_4$, broken at the electroweak scale, while the second is renormalizable and based on the Abelian gauge group $L_{\mu }-L_{\tau }$. Within the models we find characteristic predictions for other non-standard Higgs decay modes, charged lepton flavor violating decays and correlations of the branching ratios with neutrino oscillation parameters.